Hello,
I'm confused about the usage of the words "infamous" and
"notorious". I'm not sure if I should say "infamous for", "infamous because
of", "notorious for" or "notorious because of". Are the following sentences
grammatically correct?
1. Beijing is infamous for its air pollution.
2. Beijing is notorious for its air pollution.
3. Beijing is infamous because of its air pollution.
4. Beijing is notorious because of its air pollution.

The 'because of' sounds cluttered, clumsy, a bit learnerish to my ear (so as ever, efficiency, the parsimony of the phrasing, is usually a good rule of thumb). As for the 'for' examples, they seem OK, but my own question would actually be, why use that particular phrasing in the first place? It might be better to think of adjectives that describe the air pollution itself, directly: (As you may already know,) (T)he air pollution in Beijing is really bad. (Or indeed to change the noun to an adjective itself: Beijing['s air] is very polluted).